Zusammenfassung für den Vortrag am 16.04.2013 (16:45 Uhr)Oberseminar ANALYSIS - PROBABILITY
Eviatar Procaccia (Weizmann Institute of Science)
Isoperimetry in two-dimensional percolation
Consider super-critical bond percolation on ℤ2 (the square lattice). We prove the Cheeger constant of the super-critical percolation cluster restricted to finite boxes scales a.s to a deterministic quantity. This quantity is given by the solution to the isoperimetric problem on ℝ2 with respect to a specific norm. We also prove every set achieving the Cheeger constant converges to the deterministic Wulff crystal, with respect to the same norm.
Joint work with Marek Biskup, Oren Louidor and Ron Rosenthal.